
<!DOCTYPE html>

<html xmlns="http://www.w3.org/1999/xhtml">
  <head>
    <meta charset="utf-8" />
    <title>Discrete Bubble Model Users Guide &#8212; Texas A&amp;M Oil spill / Outfall Calculator 2.1.0 documentation</title>
    <link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
    <link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
    <script id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
    <script src="../_static/jquery.js"></script>
    <script src="../_static/underscore.js"></script>
    <script src="../_static/doctools.js"></script>
    <script src="../_static/language_data.js"></script>
    <link rel="index" title="Index" href="../genindex.html" />
    <link rel="search" title="Search" href="../search.html" />
    <link rel="next" title="air_eos" href="../scripts/dbm/air_eos.html" />
    <link rel="prev" title="chemical_properties.load_data" href="../autodoc/chem/chemical_properties.load_data.html" />
   
  <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
  
  
  <meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />

  </head><body>
  

    <div class="document">
      <div class="documentwrapper">
        <div class="bodywrapper">
          

          <div class="body" role="main">
            
  <div class="section" id="discrete-bubble-model-users-guide">
<h1>Discrete Bubble Model Users Guide<a class="headerlink" href="#discrete-bubble-model-users-guide" title="Permalink to this headline">¶</a></h1>
<dl class="field-list simple">
<dt class="field-odd">Release</dt>
<dd class="field-odd"><p>2.1</p>
</dd>
<dt class="field-even">Date</dt>
<dd class="field-even"><p>Jun 05, 2020</p>
</dd>
</dl>
<div class="section" id="scripts">
<h2>Scripts<a class="headerlink" href="#scripts" title="Permalink to this headline">¶</a></h2>
<p>The class objects and method functions defined in the <cite>dbm</cite> module provide a
flexible structure to handle the chemistry and thermodynamics of mixtures.
The examples detailed below show a few of the common tasks that may be
facilitated by the <cite>dbm</cite> module.  Further examples are presented in the
following scripts distributed in the <code class="docutils literal notranslate"><span class="pre">./bin</span></code> directory with the source
code.</p>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="../scripts/dbm/air_eos.html">air_eos</a></li>
<li class="toctree-l1"><a class="reference internal" href="../scripts/dbm/co2_eos.html">co2_eos</a></li>
<li class="toctree-l1"><a class="reference internal" href="../scripts/dbm/dead_oil.html">dead_oil</a></li>
<li class="toctree-l1"><a class="reference internal" href="../scripts/dbm/equilibrium.html">equilibrium</a></li>
<li class="toctree-l1"><a class="reference internal" href="../scripts/dbm/droplet_rise.html">droplet_rise</a></li>
<li class="toctree-l1"><a class="reference internal" href="../scripts/dbm/gas_bubbles.html">gas_bubbles</a></li>
<li class="toctree-l1"><a class="reference internal" href="../scripts/dbm/hydrocarbon_drops.html">hydrocarbon_drops</a></li>
</ul>
</div>
</div>
<div class="section" id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
<p>While there are many different applications of the <cite>dbm</cite> module objects and
methods, here we focus on a few of the most common tasks.</p>
<p>The basic philosophy of the <cite>dbm</cite> module objects is to store all constant
chemical properties as object attributes (e.g., molecular weight, temperature
and pressure at the critical point, etc.) and to make the thermodynamic state
(e.g., temperature, pressure, salinity, etc.) as inputs to the object methods
(e.g., when calculating the density). Because this model is designed to work
with dissolving objects, the masses of each component in the mixture are also
taken as inputs to the methods. While mole could have been the fundamental
unit for composition, mass is used in <code class="docutils literal notranslate"><span class="pre">TAMOC</span></code>.</p>
<div class="section" id="mixture-equations-of-state">
<h3>Mixture Equations of State<a class="headerlink" href="#mixture-equations-of-state" title="Permalink to this headline">¶</a></h3>
<p>As in the scripts above for <cite>air_eos</cite> and <cite>co2_eos</cite>, the <cite>dbm.FluidMixture</cite>
object provides an interface to the Peng-Robinson equation of state for any
mixture of chemicals.</p>
<p>As an example, consider a natural gas containing the following compounds with
given mole fractions in the mixture:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">composition</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;methane&#39;</span><span class="p">,</span> <span class="s1">&#39;ethane&#39;</span><span class="p">,</span> <span class="s1">&#39;propane&#39;</span><span class="p">,</span> <span class="s1">&#39;n-butane&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">yk</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.86</span><span class="p">,</span> <span class="mf">0.06</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">])</span>
</pre></div>
</div>
<p>If the binary interaction coefficients are going to be taken as default, then
we can initialize a <cite>dbm.FluidMixture</cite> object as follows:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">dbm</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span> <span class="o">=</span> <span class="n">dbm</span><span class="o">.</span><span class="n">FluidMixture</span><span class="p">(</span><span class="n">composition</span><span class="p">)</span>
</pre></div>
</div>
<p>This has now loaded all of the chemical properties of this mixture.  As an
example, the molecular weights of each compound are:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">M</span>
<span class="go">array([ 0.0160426,  0.0300694,  0.0440962,  0.058123 ])</span>
</pre></div>
</div>
<p>In order to compute thermodynamic properties, we must further define the
thermodynamic state and composition masses. The fundamental quantity
describing the variables of the mixture are the masses. In this example,
consider one mole of gas:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">gas</span><span class="o">.</span><span class="n">masses</span><span class="p">(</span><span class="n">yk</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">T</span> <span class="o">=</span> <span class="mf">273.15</span> <span class="o">+</span> <span class="mf">10.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">P</span> <span class="o">=</span> <span class="mf">101325.</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">=</span> <span class="mf">34.5</span>
</pre></div>
</div>
<p>The salinity is only used to calculate solubilities in water.  Consider
several common properties of interest:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">mass_frac</span><span class="p">(</span><span class="n">yk</span><span class="p">)</span>
<span class="go">array([ 0.70070791,  0.09163045,  0.08958287,  0.11807877])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">mol_frac</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="go">array([ 0.86,  0.06,  0.04,  0.04])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">density</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">)</span>
<span class="go">array([[ 0.85082097],</span>
<span class="go">       [ 0.85082097]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">partial_pressures</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">P</span><span class="p">)</span>
<span class="go">array([ 87139.5,   6079.5,   4053.,   4053.])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">fugacity</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">)</span>
<span class="go">array([[ 86918.57653329,   6027.56643121,   3997.97690862,   3977.65301771],</span>
<span class="go">       [ 86918.57653329,   6027.56643121,   3997.97690862,   3977.65301771]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">solubility</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span>
<span class="go">array([[ 0.0205852 ,  0.00434494,  0.00355051,  0.00366598],</span>
<span class="go">       [ 0.0205852 ,  0.00434494,  0.00355051,  0.00366598]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">diffusivity</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">array([  1.82558730e-09,   1.68688060e-09,   1.35408904e-09,</span>
<span class="go">         8.76029676e-10])</span>
</pre></div>
</div>
<p>For those entries above with more than one row in the output, the top row
refers to the gas phase and the bottom row refers to the liquid phase. If both
rows are identical (as in this example) there is only one phase present, and
the user generally must look at the density to determine which phase (here, we
have 0.85 kg/m^3, which is a gas).</p>
<p>If the same mixture is brought to deepwater conditions, there would be both
gas and liquid present:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">P</span> <span class="o">=</span> <span class="mf">490e5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">density</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">)</span>
<span class="go">array([[ 372.55019405],</span>
<span class="go">       [ 409.80668791]])</span>
</pre></div>
</div>
<p>These methods do not take steps necessary to make the gas and liquid in
equilibrium with each other. Instead, this function reports the density of gas
or liquid if each had the mass composition specified by <cite>m</cite>.</p>
<p>To evaluate the equilibrium composition, one must use the
<cite>dbm.FluidMixture.equilibrium</cite> method.  As an example for this mixture:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">T</span> <span class="o">=</span> <span class="mf">273.15</span> <span class="o">+</span> <span class="mf">4.1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">P</span> <span class="o">=</span> <span class="mf">49.5e5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">gas</span><span class="o">.</span><span class="n">equilibrium</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">)</span>
<span class="go">array([[ 0.01349742,  0.00168584,  0.00129938,  0.00092275],</span>
<span class="go">       [ 0.00029921,  0.00011832,  0.00046447,  0.00140217]])</span>
</pre></div>
</div>
<p>Generally, the equilibrium calculation is only meaningful when there is a
significant two-phase region of the thermodynamic space for this mixture.</p>
</div>
<div class="section" id="bubbles-or-droplets">
<h3>Bubbles or Droplets<a class="headerlink" href="#bubbles-or-droplets" title="Permalink to this headline">¶</a></h3>
<p>Bubbles and droplets in general require the same set of steps; here, we focus
on a bubble with similar composition to the mixture studied above. Both
bubbles and droplets are modeled by the <cite>dbm.FluidParticle</cite> object. The main
differences between the <cite>dbm.FluidParticle</cite> and <cite>dbm.FluidMixture</cite> objects is
that the <cite>dbm.FluidParticle</cite> can only have one phase (e.g., gas or liquid) and
also contains shape information so that concepts like rise velocity have
meaning.</p>
<p>If we consider the same mixture as above:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">composition</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;methane&#39;</span><span class="p">,</span> <span class="s1">&#39;ethane&#39;</span><span class="p">,</span> <span class="s1">&#39;propane&#39;</span><span class="p">,</span> <span class="s1">&#39;n-butane&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">yk</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.86</span><span class="p">,</span> <span class="mf">0.06</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">dbm</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bub</span> <span class="o">=</span> <span class="n">dbm</span><span class="o">.</span><span class="n">FluidParticle</span><span class="p">(</span><span class="n">composition</span><span class="p">,</span> <span class="n">fp_type</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
</pre></div>
</div>
<p>We can specify the thermodynamic state similarly to before (though, consider
a hot reservoir fluid in deep water):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">T</span> <span class="o">=</span> <span class="mf">273.15</span> <span class="o">+</span> <span class="mf">125.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">P</span> <span class="o">=</span> <span class="mf">150.0e5</span>
</pre></div>
</div>
<p>The mass vector is now conceptually the masses of each component in a
single bubble or droplet.  Typically, we know the mole or mass fractions of
the components of the bubble or droplet and a characteristic fluid particle
size.  Hence, the method <cite>dbm.FluidParticle.masses_by_diameter</cite> is very
helpful for determining the actual masses of each component in the mixture:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">bub</span><span class="o">.</span><span class="n">masses_by_diameter</span><span class="p">(</span><span class="mf">0.005</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">yk</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span> <span class="n">m</span>
<span class="go">[  4.54192150e-06   5.93939802e-07   5.80667574e-07   7.65375279e-07]</span>
</pre></div>
</div>
<p>Once the masses <cite>m</cite> are known, it is a simple matter to determine the
particle physical and transport attributes:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Ta</span> <span class="o">=</span> <span class="mf">273.15</span> <span class="o">+</span> <span class="mf">4.1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Sa</span> <span class="o">=</span> <span class="mf">35.4</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bub</span><span class="o">.</span><span class="n">density</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">)</span>
<span class="go">99.036200340444182</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bub</span><span class="o">.</span><span class="n">particle_shape</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">(2,                          # 2 : ellipsoid</span>
<span class="go"> 0.0050000000000000018,      # de</span>
<span class="go"> 99.036200340444182,         # rho_p</span>
<span class="go"> 1034.959691281713,          # rho_sw</span>
<span class="go"> 0.0015673283914517876,      # mu_sw</span>
<span class="go"> 0.05298375)                 # sigma</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bub</span><span class="o">.</span><span class="n">slip_velocity</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">0.22624243729143373</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bub</span><span class="o">.</span><span class="n">surface_area</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">7.8539816339744881e-05</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bub</span><span class="o">.</span><span class="n">mass_transfer</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">array([  5.32070503e-05,   5.13189189e-05,   4.38949373e-05,</span>
<span class="go">         3.14623966e-05])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bub</span><span class="o">.</span><span class="n">heat_transfer</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">array([ 0.00113312])</span>
</pre></div>
</div>
</div>
<div class="section" id="insoluble-fluid-particles">
<h3>Insoluble Fluid Particles<a class="headerlink" href="#insoluble-fluid-particles" title="Permalink to this headline">¶</a></h3>
<p>Sometimes either a particle is truly insoluble on the time-scale of the
simulations (e.g., sand) or the composition is too complicated for the
Peng-Robinson equation of state and it is safe to neglect solubility (e.g.,
for a dead oil over short time scales). In this case, an
<cite>dbm.InsolubleParticle</cite> object is a simple means to capture the critical
properties of the particle yet provide an interface to the physics methods,
such as slip velocity.</p>
<p>Consider a sand particle.  This particle is insoluble and incompressible.
The <cite>dbm</cite> module can describe this particle as follows:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">dbm</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">sand</span> <span class="o">=</span> <span class="n">dbm</span><span class="o">.</span><span class="n">InsolubleParticle</span><span class="p">(</span><span class="n">isfluid</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">iscompressible</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="go">                                 rho_p=2500.)</span>
</pre></div>
</div>
<p>Again, the mass must be established before the properties of the particle
can be interrogated:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">T</span> <span class="o">=</span> <span class="mf">273.15</span> <span class="o">+</span> <span class="mf">10.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">P</span> <span class="o">=</span> <span class="mf">10.0e5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Ta</span> <span class="o">=</span> <span class="mf">273.15</span> <span class="o">+</span> <span class="mf">4.1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Sa</span> <span class="o">=</span> <span class="mf">35.4</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">sand</span><span class="o">.</span><span class="n">mass_by_diameter</span><span class="p">(</span><span class="mf">0.005</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span> <span class="n">m</span>
<span class="go">0.000163624617374</span>
</pre></div>
</div>
<p>Then, all of the fluid properties relevant to an insoluble particle can
be calculated:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">sand</span><span class="o">.</span><span class="n">density</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">2500.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">sand</span><span class="o">.</span><span class="n">particle_shape</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">(4,                           # 4 : rigid sphere</span>
<span class="go"> 0.005000000000000002,        # de</span>
<span class="go"> 2500.0,                      # rho_p</span>
<span class="go"> 1028.5585666971483,          # rho_sw</span>
<span class="go"> 0.0015673283914517876,       # mu_sw</span>
<span class="go"> 0.07423)                     # sigma</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">sand</span><span class="o">.</span><span class="n">slip_velocity</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">0.4452547003124989</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">sand</span><span class="o">.</span><span class="n">surface_area</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">7.853981633974488e-05</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">sand</span><span class="o">.</span><span class="n">heat_transfer</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Sa</span><span class="p">,</span> <span class="n">Ta</span><span class="p">)</span>
<span class="go">array([ 0.00155563])</span>
</pre></div>
</div>
</div>
</div>
</div>


          </div>
          
        </div>
      </div>
      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
        <div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="../index.html">Texas A&M Oil spill / Outfall Calculator</a></h1>








<h3>Navigation</h3>
<ul class="current">
<li class="toctree-l1 current"><a class="reference internal" href="../user_manual.html">TAMOC User Manual</a></li>
<li class="toctree-l1"><a class="reference internal" href="../unit_tests.html">Unit Tests</a></li>
<li class="toctree-l1"><a class="reference internal" href="../glossary.html">Glossary</a></li>
</ul>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../bugs.html">Reporting Bugs</a></li>
<li class="toctree-l1"><a class="reference internal" href="../readme.html">Read Me File</a></li>
<li class="toctree-l1"><a class="reference internal" href="../release.html">Release Notes</a></li>
<li class="toctree-l1"><a class="reference internal" href="../license.html">License</a></li>
</ul>

<div class="relations">
<h3>Related Topics</h3>
<ul>
  <li><a href="../index.html">Documentation overview</a><ul>
  <li><a href="../user_manual.html">TAMOC User Manual</a><ul>
      <li>Previous: <a href="../autodoc/chem/chemical_properties.load_data.html" title="previous chapter">chemical_properties.load_data</a></li>
      <li>Next: <a href="../scripts/dbm/air_eos.html" title="next chapter">air_eos</a></li>
  </ul></li>
  </ul></li>
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
  <h3 id="searchlabel">Quick search</h3>
    <div class="searchformwrapper">
    <form class="search" action="../search.html" method="get">
      <input type="text" name="q" aria-labelledby="searchlabel" />
      <input type="submit" value="Go" />
    </form>
    </div>
</div>
<script>$('#searchbox').show(0);</script>








        </div>
      </div>
      <div class="clearer"></div>
    </div>
    <div class="footer">
      &copy;2020, Scott A. Socolofsky.
      
      |
      Powered by <a href="http://sphinx-doc.org/">Sphinx 2.4.4</a>
      &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
      
      |
      <a href="../_sources/guides/dbm.rst.txt"
          rel="nofollow">Page source</a>
    </div>

    

    
  </body>
</html>